Calculus is a branch of mathematics that deals with the study of continuous change. It was first developed with perfection by Isaac Newton in the seventeenth century. In the beginning, it was called infinitesimal calculus which later got generalized as Calculus.
Calculus is further divided into two sub-branches:
This branch of calculus deals with the concepts of integrals and their applications. It mainly deals with the solving of anti-derivatives. We formulate definite integrals by solving the anti-derivatives mainly involving volumes, lengths, and areas.
This branch of calculus deals with the concepts of derivatives and its applications. The derivatives take a function as their input and deliver another function as output. It mainly revolves around problems dealing with the rate of change like for example, the rate of change of velocity.
Now, to develop our knowledge about calculus and to understand the concepts thoroughly, we need the help of good books. Books that is good with the fundamentals and advanced concepts which give us an overall understanding of the subject. Let me suggest some of the best books to gain your knowledge about calculus. These books are amazing and would help you build your knowledge about calculus right from the foundation.
Calculus Made Easy
This book was written by the late Silvanus P Thompson in the year 1910. It is one of the most well-known books on calculus. It is considered an all-time classic.
Just like what the title says, this book makes calculus very easy. I am really bad at Math generally and Calculus has always been so alien to me, but when I read this one it was easy to grasp. He wrote in a very witty style which provokes interest in readers of every background. He wanted to make the learning process a fun-filled activity rather than the usual style which the other writers follow when it comes to Mathematics is usually bland and will not provoke interest that easily.
Most books usually have a lot of pages which itself would cause a sense of weariness in the reader but this book does not have a monstrous number of pages, it is very sharp and crisp. It is one of the best books to kick start your learning journey of calculus. It will build a very strong foundation for learning more complex applications in calculus as you progress.
It is also a great book to look out for if you wish to teach calculus to children. Usually, children will get easily bored in mathematics as it is full of numbers and looks so grim. By using this book as the teaching material you could adapt to the witty style of the author, children would love something which is taught with fun.
The book first introduces us to what integrals are and proceeds to teach infinitesimals and also takes time to explain why they are interesting. He then proceeds to differentiate, introducing us to the various formulas one by one and then he teaches us how to apply the knowledge gained from it to learn integration and its methods.
Give it a read. You will fall in love with the world of calculus.
The Calculus Lifesaver: All the Tools You Need to Excel at Calculus
This book is written by Adrian Banner, in the year 2005. It is one of the best books available on the market at about calculus. Just like the book I said about above, this book is also very user-friendly and has helped a lot of students to gain amazing results. Adrian Banner got the idea of writing this book after he developed a course on calculus at Princeton University, which focused on improving the grades of students who got average marks in calculus. If you are interested in learning this course, it is available on the internet for free as videotaped lectures. These lectures will help you gain a better understanding of calculus.
This book also has a writing style that wants to make the reader have a very fun-filled ride. It makes the read a lot less dry compared to the other books. It makes calculus look less intimidating than it usually is. It explains all the concepts and functions theoretically so that the reader will have a thorough understanding of the concepts. There are a lot of hints provided in every chapter which will be very helpful for the students.
The book does not have many solved problems so it is best to use this as a supplementary with another calculus book that has more solved examples. But it does have the necessary amount of clear-cut examples to prepare us to solve different problems. The book explains in detail on various topics like Trigonometry, functions, exponentials, and logarithms.
Adrian Banner explains in detail on how to approach a problem in a very systematic way. In each of the examples he has provided, he provides an elaborate solution, he never skips any of the steps. He also elaborates on the reasoning behind those solutions. The main aim of the book is to improve the problem-solving capabilities of the students. The examples range from easy to difficult to give us the capability of solving complex problems.
This book was written by Michael Spivak in the year 1967. It is one of the most widely recognized textbooks on calculus. It is being used as a guide for learning calculus all over the world. It is one of the best books to get introduced to one-variable calculus.
This book is a bit different than the other two books we discussed earlier, it takes a lot of time to understand the concepts and the theory behind them, but if you put in a little bit of effort, you will love the journey. It is better to first read the book ‘Calculus Made Easy’ so that you can get a clear overall picture because this book is much complex and you would find it hard to follow if you do not know the fundamentals.
The book covers a very wide plethora of topics when compared to other books we discussed before. Spivak only covers topics that are important in the journey of learning calculus and omits all other unnecessary topics, unlike the other others. The book is very well structured and precise.
The book also provides all the necessary tools to study other branches of mathematics using calculus. Many theorems have been given throughout the book with proof which other authors usually omit. Every topic is covered with elaborateness and rigor. At the end of every topic, many examples are provided with clear cut steps and the logic behind each solution is also provided and explained with much care and thought put into it.
This book is a must for students who are aiming to get proficient in calculus. It will help you to build a very strong foundation in calculus and will greatly improve your approach in solving complex problems.
Calculus is a significant topic in math taught to students after they have finished with the primary elementary education.
Calculus is not easy, but it is imperative. It has multiple applications in the field of both physics and chemistry.
I have listed the top 5 calculus books here.
Essential Calculus: Early Transcendentals
The textbook by James Stewart
As far as the calculus text is considered, this seems to be one of the best options. Many people struggle with learning numbers and buy an insane amount of books to master mathematics. However, this one offers a clear and concise explanation of calculus and its concepts.
The problems for homework are consistent and include some more challenging issues to encourage a better depth of what was just taught
Most of the books lack great explanations but not “Essential Calculus.” This book has done a great job explaining the inner workings before listing the various evolution of shortcuts found in calculus. The examples are very well explained.
The chapters are mostly well written. It seems that there are no typos or mistaken figures, as in other high school textbooks. The weakest point of the book are the proofs, which are sometimes unnecessary and necessary. These can be skipped in the next editions.
It is recommended to buy the well-written and indispensable student solutions manual for the book. The real learning comes from practicing many problems.
Each section makes a great start with an explanation, then proceeds to give five to six examples. Moreover, it consists of almost 50 problems to practice. The end of the textbook contains the rules, the list of integrals, and much more helpful information. The solution manual that comes along with this book is extremely helpful. “Essential Calculus” has only contained odd answers for the section exercises, whereas the solution manual has the working for both odd and even problems.
Graphical, Numerical, Algebraic
By Ross L. Finney and 2 more
This book does an excellent job explaining both the “how’s” and the “Why’s” of beginning calculus. There are a total of 10 chapters. The first seven chapters are meant to cover Calculus 1. I think they include relevant detail, and the problems are informative and exciting. Chapters 8 and 9 are supposed to cover the second year calculus or basics of advanced calculus. In my opinion, the lack of explanation and cramped writing, particularly in chapter 9, are degrading the book’s effort on illustrating proper calculus instruction.
This is a book tailored for the AP examination and binds to the curriculum articulated by the College Board. This textbook is handy for mastering the topics that are required to score high in the test. The book is loaded with explanations, examples, and appropriate proofs to justify the theorems. The exercises are fundamental and beneficial. The end of chapter reviews covers a wide range of graphical, tabular, and methods.
Significant examples of a function not having a limit are depicted in a cute window representing a graphing calculator.
I think “Graphical, Numerical, Algebraic” gets to the major points in a more straightforward and less obscured approach. Briefly, this book is better for students intending to major in Engineering.
The Calculus Lifesaver
By Adrian Banner
The “Calculus Lifesaver” mixes readability and ease of use with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable textbook recommended for any student seeking to master calculus.
It serves as a great help to any single-variable calculus textbook.
The book is a little informal and entertaining, but not intimidating.
The book contains more than 475 examples, ranging from easy to hard. They provide step-by-step reasoning for every case and type of question framed. The theorems and methods are justified, and their connections are made to actual practice problem-solving skills.
Complex topics such as infinite series and improper integrals are covered in detail. This is essentially an excellent book to enhance basic calculus skills. Adrian Banner has covered much of the topics you will see in Calculus I and II. The topics include limits, derivatives, graphs, optimization, and linearization problems. The list also includes L’Hopital’s Rule,, improper integrals, techniques of integration, the series problems, and the power series problems. More topics like Taylor polynomials, parametric equations and polar coordinates, arc lengths and surface areas, and also included in the book. The textbook ends with a chapter on differential equations but only a brief introduction. In the appendix, we are provided with the proofs for the theorems, understandable to those inclined to learn it. The book is lengthy, with over 700 pages.
This book is one of the best books to learn the complexities of calculus, I have come across. Adrian Banner takes you to step by step through the complete process of solving the problems. The explanations are apparent and subtle. Solutions are provided for almost all the sample problems. This is a must-read book for those who want to study and implement calculus.
The Humongous Book of Calculus Problems
By W. Michael Kelley
The book has almost 1,000 problems with fully comprehensive solutions. There are annotated notes throughout the text, explicitly clarifying what is being asked. The answers are detailed. Extra explanations are provided to make the theorems and topics clear. The textbook also contains pointers to other problems that show the skills you will need.
The major topics are limits, continuity, derivatives, tangent lines, integrals, velocity, area, volume, acceleration, and infinite series. Not only easy and medium but the tough stuff like epsilon-delta proofs and formal Riemann sums are also present in the book. This book is a great resource. However, it is a problem-solving book. It consists of solved calculus problems. Plus, it is not a workbook where you can solve the problems and then check their solutions at the back. You could choose to cover up the solution steps on the page while you work the answer yourself. The path to success in math is working and understanding problems. The more you practice the better chance you have to do well at tests.
The benefit of the book is that it shows all the steps of a solution in a more detailed form than most other guides. The author has also doodled additional helpful tips in the margins of the problems. The skull icon on specific issues depicts that they are especially challenging problems.
Calculus Made Easy
Book by Silvanus P. Thompson
Calculus Made Easy is one of the most popular calculus books. This textbook makes the subject more understandable and comprehensible to readers of all levels. The book is infused with a new introduction, three additional chapters, modernized language, and specific methods. In the end, an appendix of enjoyable and challenging practice problems are listed. Calculus Made Easy has been tailored for modern readers.
“Calculus Made Easy is arguably the best math teaching ever. To a non-mathematician, its simplicity and clarity reveal the mathematical genius of Newton, Leibniz, and Thompson himself. Martin Gardner deserves huge thanks for renewing this great book.” Julian Simon, author of Population Matters.
R.L. Graham, the Chief Scientist of AT&T Labs, complimented the author for writing it. He called it a remarkable and user-friendly approach to the study of calculus. The book is furnished by Martin Gardner, one of the most highly acclaimed mathematical expositor. This book really justifies its title – Calculus made easy. The book is easy to understand with a little effort. You will enjoy reading the book and gain a valuable understanding of calculus from it.
This is an old book slightly revised by Gardner. The introduction and some materials are intriguing. This book has a dearth of examples when compared to other modern textbooks. I would not recommend this book if you are not much interested in the historical approach.
These three books together will make you very proficient in calculus and will take you to the next level. Through these three books, I gained a lot of knowledge and get an overall understanding of the subject. Have a happy fun-filled journey reading these beautiful books.